This is what i've done so far:Evaluate the integral
Hint: Write the integrand as an integral.
This was to just get my bearings with what the integral should look like.
In double integral form, the initial integral is:
Call the region we're integrating over R.
Let and .
.
This gives:
Integrating by parts gives:
Firstly, is this answer correct?
Secondly, is there an easier way to do it than this??
That's probably a better way of doing it
The reversal is the same as what I reversed previously so the integral is now (where y=t).
Let
Which is the same as before.
Well that was a good way of doing it, but can't you do the initial integral without splitting it up into two double integrals?
I have no idea, I only did it this way because this is how the question wanted me to do it.
Perhaps there exist some integrals that can only be solved by turning them into double integrals. If you look at the second method, is never integrated directly.
I can't actually think of any integrals that can only be solved by turning them into a double integral, so i'm only really speculating about where this method would be useful.